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Generalization of the power means and their inequalities. (English) Zbl 0753.26009

The paper contains a generalization of the power means which includes a class of positive nonlinear functionals. For these new means the author obtains generalizations of the fundamental mean inequality, Hölder’s, Minkowski’s and related inequalities.

MSC:

26D15 Inequalities for sums, series and integrals
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References:

[1] Beesack, P. R.; Pečarić, J. E., On Jessen’s inequality for convex functions, J. Math. Anal. Appl., 110, 536-552 (1985) · Zbl 0591.26009
[2] Pečarić, J. E.; Beesack, P. R., On Jessen’s inequality for convex functions, II, J. Math. Anal. Appl., 118, 125-144 (1986) · Zbl 0608.26010
[3] Pečarić, J. E., On Jessen’s inequality for convex functions, III, J. Math. Anal. Appl., 156, 231-239 (1991) · Zbl 0743.26018
[4] You, Guang-Rong, On Hölder’s inequalities for convexity, J. Math. Anal. Appl., 143, 448-458 (1989) · Zbl 0688.26010
[5] Mitrinović, D. S.; Pečarić, J. E., Generalizations of the Jensen inequality, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 196, 21-26 (1987), Heft 1-3 · Zbl 0639.26009
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